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Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory

Author

Listed:
  • Simone Fiori

    (Department of Information Engineering, Marches Polytechnic University, 60121 Ancona, Italy)

  • Luca Bigelli

    (Graduate School of Mechatronic Engineering, Politecnico di Torino, 10129 Turin, Italy)

  • Federico Polenta

    (Graduate School of Automation and Control Engineering, Politecnico di Milano, 20133 Milan, Italy)

Abstract

The aim of the present research work is to design a control law for a quadcopter drone based on the Virtual Attractive-Repulsive Potentials (VARP) theory. VARP theory, originally designed to enable path following by a small wheeled robot, will be tailored to control a quadcopter drone, hence allowing such device to learn flight planning. The proposed strategy combines an instance of VARP method to control a drone’s attitude ( SO ( 3 ) -VARP) and an instance of VARP method to control a drone’s spatial location ( R 3 -VARP). The resulting control strategy will be referred to as double-VARP method, which aims at making a drone follow a predefined path in space. Since the model of the drone as well as the devised control theory are formulated on a Lie group, their simulation on a computing platform is performed through a numerical analysis method specifically designed for these kinds of numerical simulations. A numerical simulation analysis is used to assess the salient features of the proposed regulation theory. In particular, resilience against shock-type disturbances are assessed numerically.

Suggested Citation

  • Simone Fiori & Luca Bigelli & Federico Polenta, 2022. "Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory," Mathematics, MDPI, vol. 10(7), pages 1-37, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1104-:d:782261
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    References listed on IDEAS

    as
    1. Simone Fiori, 2019. "Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors," Mathematics, MDPI, vol. 7(10), pages 1-35, October.
    2. Yong-bo Chen & Guan-chen Luo & Yue-song Mei & Jian-qiao Yu & Xiao-long Su, 2016. "UAV path planning using artificial potential field method updated by optimal control theory," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1407-1420, April.
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    Cited by:

    1. Durán-Delfín, J.E. & García-Beltrán, C.D. & Guerrero-Sánchez, M.E. & Valencia-Palomo, G. & Hernández-González, O., 2024. "Modeling and Passivity-Based Control for a convertible fixed-wing VTOL," Applied Mathematics and Computation, Elsevier, vol. 461(C).

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